If both the linear relationship and current emission trends hold into the future, the study suggests the Arctic will be ice free by 2045—far sooner than some climate models predict. The study suggests that those models are underestimating how warm the Arctic has already become and how fast that melting will proceed. And it gives the public and policymakers a concrete illustration of the consequences of burning fossil fuels, says Edward Maibach, director of the Center for Climate Change Communication at George Mason University in Fairfax, Virginia. "Concrete information is always more engaging than abstract information," he says.

According to the new calculations, for instance, the average annual carbon emissions from a U.S. family of four would claim nearly 200 square meters of sea ice. Over 3 decades, that family would be responsible for destroying more than an American football field's worth of ice—a tangible threat to ice-dependent creatures such as polar bears. The study also makes for vivid comparisons between nations: Each person in the United States, for instance, is responsible for the destruction of 10 times as much ice each year as someone in India.

On thin ice

Based on CO2 emissions in 2013, each U.S. resident led to the melting of 49 square meters of Arctic sea ice—nearly 10 times as much as someone in India.

J. You/Science

Sea ice retreat is already a poster child for global warming, and some earlier studies had shown that the retreat closely tracks atmospheric CO2 levels. But Notz and co-author Julienne Stroeve, an expert in sea ice satellite measurements at the National Snow and Ice Data Center in Boulder, Colorado, identified a tighter link to human activity by compiling annual human-caused greenhouse gas emissions and comparing those numbers with historic observations of Arctic sea ice coverage during September—when sea ice is at its smallest. To avoid problems with year-to-year ice fluctuations, they used a 30-year moving average of ice coverage, allowing them to study the years from 1968 to 2000.

To see whether the linear relationship they found between emissions and sea ice also emerged in computer simulations, they checked 36 of the world's major climate models. In simulations in which CO2 levels rose 1% every year, they found the same telltale pattern every time, Stroeve says. Yet the models' sensitivity was off: They tended to underestimate the amount of ice loss. "Models are not perfect," Stroeve says. "And if you can use observations by themselves to forecast when Arctic ice will go away maybe that's in some ways better."

By tracing the trajectory of their observations into the future, Stroeve and Notz estimate that another 1000 gigatons of CO2 would push summer sea ice coverage to below 1 million square kilometers, an area the size of Texas and New Mexico combined. That's essentially ice free, because the remaining ice would be tucked into pockets around places like the northern edge of Greenland, where winds concentrate ice. If today's carbon emissions of 35 gigatons per year persist, that translates to an ice-free ocean, at least in summer, by about 2045. Scientists say the same 1000 gigatons that would erase sea ice would also warm the world by 2°C—the threshold that the Paris climate agreement intends to stay below.

Stroeve and Notz aren't certain why the shrinking of the sea ice tracks emissions so neatly. But they point to a simple potential explanation: As rising emissions warm the Arctic air, the ice retreats to more northerly latitudes, where there is less heat from incoming direct sunlight. Notz thinks that climate models tend to downplay the amount of sea ice lost to each ton of CO2 because they're underestimating how warm the Arctic is getting. Although that might seem easy to check, data for air temperature over the Arctic sea ice is quite sparse, says Gregory Flato, a sea ice scientist at the Canadian Centre for Climate Modelling and Analysis in Victoria.

Alexandra Jahn, a sea ice modeler at the University of Colorado in Boulder, says Stroeve and Notz's mechanism "finally explains this linear relationship that people have been seeing, but didn't have a physical explanation for." But she thinks further studies are needed to rule out other factors that might influence sea ice decline, such as changes in cloud cover. Stroeve and Notz say the impact of clouds and ocean temperatures aren't significant.

They do acknowledge, however, that sea ice half a world away in the Antarctic doesn't track emissions as faithfully. There, forces including wind and ocean temperatures have a stronger impact on sea ice behavior, they say.

François Massonnet, a sea ice modeler at the Barcelona Supercomputing Center in Spain, cautions against assuming that what happened in the recent past will last into the future. A curveball, such as a shift in the amount of CO2 the oceans can absorb, could upset the pattern by breaking the correlation between emissions and Arctic warming. "It's tempting, but it's very dangerous to be too confident that we can extrapolate linear relationships," he says. "We know that the Arctic climate is very nonlinear."